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2
Biochemistry
Enzyme kinetics
Description of Module
Subject Name Biochemistry
Paper Name
Module Name/Title Enzyme Kinetics
Dr. Vijaya Khader Dr. MC Varadaraj
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Biochemistry
Enzyme kinetics
1. Objectives
2. Enzymes as biological catalyst 3. Enzyme Catalysis 4. Understanding enzyme Kinetics 5. Equations for enzyme kinetics 6. Multisubstrate system 7. Enzyme Inhibition
2. Enzymes
Enzymes (proteins) catalyze a chemical reaction that takes place within a cell (but not always). All proteins,
including enzymes are synthesized by ribosomes.
Enzymes are of primary importancein carrying out metabolic pathways, which otherwise would require high
amount of energy (heat) in processing chains of chemical reaction, but enzymes (highly specific for substrate
and reaction type)help to pull off these reactions at higher rate and at mild temperature and pressure.
An enzyme by joining with its specific substrate lowers the energy required for activation of that particular
reaction (Activation energy). The reaction occurs, and the enzyme is released again unchanged to be used
again.
3. Enzyme catalysis
CATALYST: it can be defined as any substance which performs its function by enhancing the reaction rate
without itself being consumed as after the reaction completes, catalyst is now free for another reaction. A
reaction which is driven by a catalyst is termed as catalyzed reaction, and the process is known as catalysis.
Catalyst has certaincharacteristics described below:
1. It provides a different mechanism for the reaction and lowers the Gibbs energy of activation.
2. Initially an intermediate is formed with the reactant(s) by a catalyst which is released later on during the
product formation step.
3. The catalyst cannot alter the thermodynamic equilibrium constant, which means that it is not able affect the
enthalpies or Gibbs energies of both the reactants and products.
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Biochemistry
Enzyme kinetics
Fig.1 Gibb’s energy in (a)Uncatlyzed reaction.(b)Catalyzed reaction. rGo remains same in both cases.
Enzymes escalate chemical reaction without itself being chemically transformed and they also do not alter the
equilibrium of the reaction. Alternative reaction pathways with lower energy barriers are introduced by
enzymes for catalysis.Catalytic Action: Enzyme accelerates the rate of the reaction without shifting or changing
its equilibrium, and in order to understand this "Transition state theory" (Eyring, 1935) was given which
suggests, Reactants must overcome an energy barrier and pass through an activated complex before moving
on to the reaction products.
A ⇌ B, can be designated by A⇌ X ⇌ B
here, X = transition state/activated complex
Enzyme introduces alternative pathways by following mechanism:
a.) Covalent catalysis: Catalytic functional group (nucleophile) attacks the substrate and forms covalent
bond. Then electrons are withdrawn by an electrophilic catalyst resulting in rupture of the covalent
bond, permitting further reaction and regeneration of enzyme based nucleophile. Eg. Decarboxylation
of acetoacetate catalysed by primary amines.
b.) Acid base catalysis: A process involving partial proton transfer from an acid lowering the free energy of
the transition state. A reaction is base catalysed, when the reaction rate is increased by partial proton
abstraction by a base.Eg. Hydrolysis of peptide using chymotrypsin
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Biochemistry
Enzyme kinetics
c.) Proximity: The catalytic effectiveness is increased by bringing the substrate and catalytic groups closer
(thereby increasing no. of collisions and reducing entropy. Eg. Imidazole-catalysed hydrolysis of esters,
when the substrate and catalyst are brought in proximity to each other by hydrophobic interactions.
d.) Molecular distortion: The process in which the configuration of both enzyme and substrate, gets
modified, upon binding of substrate is known asinduced fit. Conformation of the substrate is changed
in a way that it resembles the transition state; the conversion into the transition state is further
facilitated by the stress created due to distortion of the substrate. The transition state is further
stabilized by tight binding with enzyme and lowering activation energy requirement.
Fig.2Energy diagram representing catalyzed and uncatalyzed reaction. In presence of catalyst (enzyme) the
activation energy is lowered (compare the peaks of catalyzed and uncatalyzed reaction).
4. Enzyme kinetics
Enzyme kinetics, deals with enzyme reactions which are time-dependent and explains the mechanisms of
enzyme catalysis and its regulation.
Let’s understand enzyme kinetics as a function for the concentration of the substrate available for the enzyme.
Start the experiment with a series of tubes which contains substrate, [S]. At time (t) zero, addsome amount of the enzyme. Wait for few minutes Then, measure the newly formed product concentration. We can also use spectrophotometer,If
product absorbs light.
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Biochemistry
Enzyme kinetics
At a time when the amount of substrate is greater than the amount of enzyme, then, the rate is the initial velocity of Vi.
If we plot Vi as a function of [S], following observations will be made:
At low [S], the initial velocity,Vi, rises linearly with increasing [S]. When [S] increases, Vi settle down (rectangular hyperbolais formed). The asymptote shows Vmax as the maximum velocity of the reaction. The substrate concentration which produces a Vi equal to one-half of Vmax is called the Michaelis-
Menten constant ( Km).
Km is (approximately) inversely related to the maximum reaction velocity, or strength of binding between the enzyme and its substrate. Lower the Km value, higher is the affinity for its substrate.
4.1 EQUATION OF ENZYME KINETICS
4.1.1 MICHAELIS MENTEN EQUATION
In 1913, Michaelis (1875–1949) and Menten (1879–1960, proceeded the work which was previously done by
Frenchchemist V Henri (1872–1940), developed a mechanism to explain how the initial rate of enzyme-
catalyzed reactions depends on the concentration.
Derivation of Michaelis-Menten equation: Few considerable assumptions can be made for the Michaelis-Menten equation derivation: • Assuming that reverse reaction (P→ S) is negligible
• Assuming, there exists only a single central complex (ES). i.e. ES breaks down to E + P.
• Considering a situation when, [S] >> [E].Then the immediate interaction of S and E to form ES does not
significantly affect free [S].
• Usually, ([S]-[ES])/[S] ≥ 99.9%
Considering the above assumptions, the reaction scheme is as follows:
Following are two parts for this reaction:
1) Formation of ES complex (a second order process)
2) The breakdown of ES complex to product P and free enzyme E (a first order process).
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Biochemistry
Enzyme kinetics
And the final Michaelis-Menten equation is as given below :
v =
Vmax[S]
[S]KM
Vmax = The maximum velocity achieved by the system, at maximum (saturating) substrate concentrations
KM (the Michaelis constant)= substrate concentration at which the reaction velocity is 50% of the Vmax. Its
unit is mM. It is also the concentration at which concentration of substrate is half the maximal velocity is
observed.
[S] = concentration of the substrate S
Fig 4.Graphical determination forVmax and KM. Line weaver burk plot
On the other hand, It is observed that in order to determine the value of Vmax , the plot of V0 vs. [S] is not useful
since tracing the value of Vmax under very high substrate concentrations is difficult. So, American chemists H.
Line weaver and Burk employed the double-reciprocal plot. These are known as the Lineweaver–Burk plot.
These are also called double-reciprocal plots.
1
V°=
K
V°[S]+
1
Vmax
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Biochemistry
Enzyme kinetics
Fig 5 Lineweaver Burk plot
KM and Vmax is achieved from intercepts and slope of the straight line from graph.
One of the drawbacks of Lineweaver–Burk plot is that it is more susceptible to error. Another disadvantage is that at high substrate concentrations, the plot tends to compresses the data points into a small region and puts more emphasis on the points at lower substrate concentrations, which are often the least accurate. Eadie–Hofstee plot To overcome the drawbacks of Lineweaver Burke Plot, the Eadie–Hofstee plot was given. Multiplying both sides of Michaelis-Menten equation by Vmax, we get,
𝑣° = −𝐾𝑚
𝑉
[𝑆]+ 𝑉𝑚𝑎𝑥
The above equation represents a plot of 𝑣° versus 𝑣°/ [S], called Eadie–Hofstee plot. The plot is a straight line with slope equal to –KM and intercepts Vmax on the 𝑣° axis and Vmax/KM on 𝑣°/[S] axis.
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Biochemistry
Enzyme kinetics
Fig.6 Eadie-Hofstee plot
SIGNIFICANCE OF KM and Vmax
In most cases, KM value for enzymes lies between 10-1 and 10-7 . Value of KM depends on particular substrate,
and environmental conditions like ionic strength, pH and temperature.
The Michaelis constant, KM has following meanings:
It is the concentration of substrate at whichhalf ofthe active site gets occupied. Therefore, KM provides
a measure of the substrate concentration which is required for the significant catalytic process.
fES refers to the fraction of sites filled. At any substrate concentration, fES can be measured when
the KM is known, from the following equation:
𝑓𝐸𝑆=
𝑉
𝑉𝑚𝑎𝑥=
[𝑆]
[𝑆]+𝐾𝑀
KM is described as (k-1 + k2)/k1. Considering a limiting case when, (k-1 >> k2), the ES complex breaks down
to E and S much more rapidly than product formation. Under these circumstances:
KM =𝑘−1
𝑘1
Dissociation constant of ES complex :
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Biochemistry
Enzyme kinetics
KES = [𝐸][𝑆]
𝐸𝑆=
𝑘−1
𝑘1
KM represents the affinity of the ES complex, only when k-1 is much greater than k2.
High KM implies weak binding, whereas a low KM implies strong binding.
Vmax gives the turnover number of an enzyme. By turnover number, it is meant the amount and number of
substrate molecules that are converted into product by an enzyme molecule in a unit time, when the enzyme is
fully saturated with substrate. It is equal to the kinetic constant k2, which is also called kcat. Vmax, explains the
turnover number of an enzyme if the concentration of active sites [E]T is known :
Vmax =𝑘2[E]T
hence, 𝑘2= Vmax /[E]T
5. Multisubstrate System:
Until now, wehave studied single substrate enzyme catalysis, but in few instances, the process involves two or
multi-substrates. Eg.
C2H5OH + NAD+↔ CH3CHO +NADH + H+
The above reaction is alcohol dehydrogenase catalyzed. Alcohol dehydrogenase enzyme binds to both
NAD+and the substrate which will be oxidized.
6. Enzyme Inhibition: Inhibitors are a class of compounds which decrease or reduce the rate of an enzyme-catalyzed reaction. By
studying enzyme inhibition, researchers have understood the nature of functional groups at the active site and
the mechanism of specificity. Enzyme activity is usually regulated by the phenomenon called feedback
mechanism where the end product is responsible for inhibiting the enzyme’s activity. Infact, the amount of
products formed is controlled by enzyme inhibition.
In irreversible inhibitions, inhibition gradually elevates with respect to time. When the irreversible inhibitor
concentration exceeds the enzyme concentration, it results in complete inhibition.
Reversible Inhibition
Reversible inhibition can be of three types
Competitive inhibition
Non-competitive inhibition, and
Uncompetitive inhibition
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Biochemistry
Enzyme kinetics
Competitive Inhibition: In this case, both the substrate S and the inhibitor I compete. Competitive inhibition
can be reversed by increasing the concentration of the substrate.
k1 k3
E + S <—> ES <—> E + P
+ k-1
I <—> EI
The Line weaver Burk equation would be:
1
𝑣°=
𝐾𝑀
𝑉𝑚𝑎𝑥( 1 +
𝐼
𝐾𝐼)
1
[𝑆]+
1
𝑉𝑚𝑎𝑥
Noncompetitive inhibition:
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Biochemistry
Enzyme kinetics
In non-competitive inhibition, the inhibitor may bind with both the free enzyme as well as the enzyme-substrate
complex. But the inhibitor binds with enzyme at a site which is distinct from the substrate binding site. The
binding of the inhibitor however does not affect the substrate binding, and vice versa. The reactions are:
The line weaver burk equation would be:
1
𝑣°=
𝐾𝑀
𝑉𝑚𝑎𝑥( 1 +
𝐼
𝐾𝐼)
1
[𝑆]+
1
𝑉𝑚𝑎𝑥( 1 +
𝐼
𝐾𝐼)
Vmax reduced by 1+ [I] / KI factor but KM is unchanged
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Biochemistry
Enzyme kinetics
Uncompetitive Inhibition :
In Uncompetitive Inhibition, an inactive ESI complex is formed when Inhibitor reversibly binds to the enzyme–
substrate [ES] complex. Here in this case inhibitor does not bind to the free enzyme.
Here in the above reaction, ESI complex does not form a product because ‘I’ does not interfere with the
formation of ES. Again, unlike competitive inhibition, uncompetitive inhibition cannot be reversed by increasing
the substrate concentration.
1
𝑣°=
𝐾𝑀
𝑉𝑚𝑎𝑥
1
[𝑆]+
1
𝑉𝑚𝑎𝑥( 1 +
𝐼
𝐾𝐼)
FIG. 7 Lineweaver–Burk plots: (a) competitive inhibition, (b) noncompetitive inhibition, and(c) uncompetitive inhibition
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